There have been recent theoretic results that provide sufficient conditions for the existence of a species displaying absolute concentration robustness (ACR) in a power law kinetic (PLK) system. One such result involves the detection of ACR among net
works of high deficiency by considering a lower deficiency subnetwork with ACR as a local property. In turn, this smaller subnetwork serves as a building block for the larger ACR-possessing network. Here, with this theorem as foundation, we construct an algorithm that systematically checks ACR in a PLK system. By slightly modifying the algorithm, we also provide a procedure that identifies balanced concentration robustness (BCR), a weaker form of concentration robustness than ACR, in a PLK system.
Absolute concentration robustness (ACR) is a condition wherein a species in a chemical kinetic system possesses the same value for any positive steady state the network may admit regardless of initial conditions. Thus far, results on ACR center on ch
emical kinetic systems with deficiency one. In this contribution, we use the idea of dynamic equivalence of chemical reaction networks to derive novel results that guarantee ACR for some classes of power law kinetic systems with deficiency zero. Furthermore, using network decomposition, we identify ACR in higher deficiency networks (i.e. deficiency $geq$ 2) by considering the presence of a low deficiency subnetwork with ACR. Network decomposition also enabled us to recognize and define a weaker form of concentration robustness than ACR, which we named as `balanced concentration robustness. Finally, we also discuss and emphasize our view of ACR as a primarily kinetic character rather than a condition that arises from structural sources.
